Pertanyaan

Diketahui dan . Jika p → adalah vektor proyeksi ortogonal a → pada b → dan q adalah vektor proyeksi ortogonal b pada a ,maka p ⋅ q = ....

Diketahui begin mathsize 14px style italic a with italic rightwards arrow on top equals open parentheses table row 1 row 3 row cell negative sign 4 end cell end table close parentheses end style dan . Jika $p \to$ adalah vektor proyeksi ortogonal $a \to$ pada $b \to$ dan $q$ adalah vektor proyeksi ortogonal $b$ pada $a$ , maka $p \cdot q =$ ....

$begin mathsize 14px style negative sign fraction numerator 2.600 over denominator 247 end fraction end style$
$begin mathsize 14px style negative sign fraction numerator 2.000 over denominator 247 end fraction end style$
$begin mathsize 14px style fraction numerator 2.000 over denominator 247 end fraction end style$
$begin mathsize 14px style fraction numerator 2.600 over denominator 247 end fraction end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Karena adalah vektor proyeksi ortogonal pada , maka Selanjutnya, karena adalah vektor proyeksi ortogonal pada , maka Jadi, Jadi, jawaban yang tepat adalah D.

Karena adalah vektor proyeksi ortogonal pada , maka

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Selanjutnya, karena adalah vektor proyeksi ortogonal pada , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell italic p with rightwards arrow on top end cell equals cell open parentheses fraction numerator italic a with rightwards arrow on top ⋅ italic b with rightwards arrow on top over denominator open vertical bar italic a with rightwards arrow on top close vertical bar squared end fraction close parentheses italic a with rightwards arrow on top end cell row blank equals cell open parentheses fraction numerator open parentheses table row 1 row 3 row cell negative sign 4 end cell end table close parentheses ⋅ open parentheses table row cell negative sign 3 end cell row 5 row cell negative sign 2 end cell end table close parentheses over denominator open parentheses square root of 1 squared plus 3 squared plus open parentheses negative sign 4 close parentheses squared end root close parentheses squared end fraction close parentheses open parentheses table row 1 row 3 row cell negative sign 4 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator 1 ⋅ open parentheses negative sign 3 close parentheses plus 3 ⋅ 5 plus open parentheses negative sign 4 close parentheses ⋅ open parentheses negative sign 2 close parentheses over denominator open parentheses square root of 1 plus 9 plus 16 end root close parentheses squared end fraction close parentheses open parentheses table row 1 row 3 row cell negative sign 4 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator negative sign 3 plus 15 plus 8 over denominator open parentheses square root of 26 close parentheses squared end fraction close parentheses open parentheses table row 1 row 3 row cell negative sign 4 end cell end table close parentheses end cell row blank equals cell 20 over 26 open parentheses table row 1 row 3 row cell negative sign 4 end cell end table close parentheses end cell row blank equals cell 10 over 13 open parentheses table row 1 row 3 row cell negative sign 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 10 over 13 end cell row cell 30 over 13 end cell row cell negative sign 40 over 13 end cell end table close parentheses end cell end table end style$

Jadi,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell italic p with rightwards arrow on top ⋅ italic q with rightwards arrow on top end cell equals cell open parentheses table row cell negative sign 30 over 19 end cell row cell 50 over 19 end cell row cell negative sign 20 over 19 end cell end table close parentheses ⋅ open parentheses table row cell 10 over 13 end cell row cell 30 over 13 end cell row cell negative sign 40 over 13 end cell end table close parentheses end cell row blank equals cell open parentheses negative sign 30 over 19 close parentheses ⋅ 10 over 13 plus 50 over 19 ⋅ 30 over 13 plus open parentheses negative sign 20 over 19 close parentheses ⋅ open parentheses negative sign 40 over 13 close parentheses end cell row blank equals cell negative sign 300 over 247 plus fraction numerator 1.500 over denominator 247 end fraction plus 800 over 247 end cell row blank equals cell fraction numerator 2.000 over denominator 247 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah D.